This application claims the priority of the European patent application No. 99 810 381.6, filed on May 4, 1999, the disclosure of which is incorporated herein by reference in its entirety.
The invention refers to the field of magnetic force or Hall probe microscopy. It is based on a method for calibrating a magnetic force microscope (MFM) or a scanning Hall probe microscope (SHPM), wherein a raw MFM- oder SHPM-image S is measured by scanning a sample with a microscopic tip and an instrument response function IRF is determined for calibrating the MFM or SHPM.
The invention relates to a state of the art as presented in the article of J.-G. Zhu et al., xe2x80x9cMagnetic force microscopy image restoration technique for removing tip dependencexe2x80x9d, Journal of Applied Physics Vol. 83 (11), p. 6223-6225 (1998). It is proposed to use samples that approximate a point source of magnetic field, i. e. a magnetic monopole or dipole, in order to determine an impulse response function of the magnetic force microscope (MFM) tip. The impulse response function is then used to deconvolve raw MFM-images in the Fourier space. This method has severe drawbacks. The better the sample approximates a point source the smaller the MFM-signal will be. This severely limits the accuracy of the calibration, due to the small signal-to-noise ratio of the measurement. Moreover, point source samples are difficult to produce. Their spatial extent limits the accuracy to which the impulse response function can be determined. For repeated calibrations repeated positioning of the point source sample is necessary.
Principles of operation of MFMs are shown in the article of D. Rugar et al., xe2x80x9cMagnetic force microscopy: General principles and applications to longitudinal recording mediaxe2x80x9d, Journal of Applied Physics, Vol. 68 (3), P. 1169-1183 (1990). The MFM response is analyzed in direct space by modelling the tip geometry and cantilever tilt. However, the geometric tip model is complicated and of limited value since four fitting parameters are used.
Another tip calibration technique is presented in the article of L. Kong et al., xe2x80x9cQuantification of magnetic force microscopy using a micronscale current ringxe2x80x9d, Applied Physics Letters Vol. 70 (15), p. 2043-2045 (1997). A controlled magnetic field of a ring conductor with 1 xcexcm-5 xcexcm diameter is probed by the tip. The resulting MFM-signal is interpreted in terms of a magnetic monopole and dipole strength of the tip. Again a tip model is required to quantify magnetic properties of the tip.
Principles of operation of Scanning Hall probe microsopes (SHPM) are shown in the article of A. Oral et al., xe2x80x9cReal-time scanning Hall probe microscopyxe2x80x9d, Applied Physics Letters Vol. 69 (9), p. 1324-1326 (1996). A tip comprising a submicron Hall probe manufactured in a GaAs heterostructure is scanned over the sample to measure the magnetic stray field using conventional scanning tunneling microscopy positioning techniques. However, the magnetic field sensitivity decreases on the length scale of the Hall probe tip and requires calibration for absolute stray field measurements.
Hence, it is a general object of the invention to provide a simplified and improved calibration method for magnetic force microscopes (MFM) and scanning Hall probe microscopes (SHPM). Now, in order to implement these and still further objects of the invention, which will become more readily apparent as the description proceeds, the calibration method comprises the steps of providing a sample with an irregular sample magnetization pattern M or an irregular current distribution over an extended area, determining, based on the raw MFM- or SHPM-image S of the sample, an approximate sample magnetization pattern M0 and therefrom an approximate sample magnetic stray field distribution H0, and calculating the instrument response function IRF from the raw MFM- or SHPM-image S and the approximate sample magnetic stray field distribution H0.
Thus one aspect of the invention resides in a method for calibrating a magnetic force microscope or a scanning Hall probe microscope, wherein raw MFM- or SHPM-images of a sample producing an arbitrary magnetic stray field are measured, the sample magnetization or current distribution patterns are estimated, the corresponding magnetic stray fields are calculated and, from the raw MFM- or SHPM-images and the magnetic stray fields, an instrument response function IRF is determined. The instrument response function IRF contains information on the magnetic stray field distribution of the tip and the tilt and mechanical behaviour of the cantilever.
By using a calibrated tip the magnitude and distribution of magnetic stray fields of arbitrary samples can be determined. Through this, also the magnetization or current distribution in the samples can be found.
The method according to invention allows to measure rather than to model the instrument response. The magnetic stray field distribution or sensitivity of the tip is determined with high precision and without restriction to magnetic monopole or dipole models. The need for preparing samples with a specific pattern of magnetic field sources is eliminated.
In another aspect of the invention the calibration method comprises the steps of determining, based on the raw MFM- or SHPM-image S, an approximate sample magnetization pattern M0 and therefrom an approximate sample magnetic stray field distribution H0, calculating Fourier space distributions of the raw MFM- or SHPM-image S(k) and of the approximate sample magnetic stray field distribution H0(k), and calculating an instrument response function IRF(k)=S(k)/H0(k). The instrument response function IRF is thus calculated by deconvolution in Fourier space of the raw MFM- or SHPM-image with the magnetic stray field.
In a further aspect of the invention the calibration method comprises the steps of: a) measuring a plurality of raw MFM or SHPM-images Si (i=1 . . . n), b) determining first approximate sample magnetization patterns Mi,0 and first approximate sample magnetic stray field distributions Hi,0, and c) calculating from Si, and Hi,0 first approximate instrument response functions IRFi,0 and averaging them to form an initial instrument response function IRF0. Thus a plurality of MFM- or SHPM-images is measured and the average of their instrument response functions delivers an improved instrument response function IRF0.
In one embodiment the preceding steps b) and c) are reiterated by using a (jxe2x88x921)-th instrument response function IRFjxe2x88x921 to recalculate magnetization patterns Mi,j, magnetic stray field distributions Hi,j and a j-th instrument response function IRFj (j=1 . . . m). In other words, based on the averaged instrument response function IRF0, an iterative calculation of approximate sample magnetization patterns, approximate sample magnetic stray field distributions and improved averaged instrument response functions IRFj (j=1 . . . m) is performed. With an increasing number of iterations j the instrument response functions IRFj converge towards a xe2x80x9ctruexe2x80x9d instrument response function.
Other embodiments refer to choosing samples with magnetization vectors oriented perpendicular to a sample surface to be scanned, to replacing the sample magnetic stray field distribution H by its derivative H,z in case of dynamic measurements, and to applying the calibration method to measure absolute values of magnetic stray fields H, magnetization patterns M or microscopic current distributions.
In further embodiments a tip calibration function qtip, characterizing the magnetic stray field distribution of the tip of a magnetic force microscope, is derived from the instrument response function IRF. The tip calibration function qtip is useful to characterize the response of integrated circuits, magnetic reading heads, Hall sensors or SQUIDS to local magnetic fields or even to generate absolute microscopic magnetic gauging fields.